Goldbach's Conjecture is True!?

qed

Senior Member
Goldbach conjecture, in number theory, is the assertion that every even counting number greater than 2 is equal to the sum of two prime numbers. 3=1+2, 4=2+2, 5=2+3, ... try it. The Russian mathematician Christian Goldbach first proposed this conjecture in a letter to the Swiss mathematician Leonhard Euler in 1742. While true for every number we have tried, in has never been proved true. Many have tried. While not a Millennium Prize Problem, it is a Holy Grail. I have tried :rolleyes: one holiday.
Recently the conjecture has been proved true by Janusz Czelakowski (who I have met at conference and have referenced). While still to be published in a journal, and hence properly peer reviewed, it has been three years in the coming, and has survived/grown-from a few rounds in the community, Stack Overflow and two rounds on Research Gate. The currently unbroken version is on Research Gate. He uses Universal Algebra (in this case Peano Arithmetic) and essentially Formal Set Theory.
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Goldbach conjecture, in number theory, is the assertion that every even counting number greater than 2 is equal to the sum of two prime numbers. 3=1+2, 4=2+2, 5=2+3, ... try it. The Russian mathematician Christian Goldbach first proposed this conjecture in a letter to the Swiss mathematician Leonhard Euler in 1742. While true for every number we have tried, in has never been proved true. Many have tried. While not a Millennium Prize Problem, it is a Holy Grail. I have tried :rolleyes: one holiday.
Recently the conjecture has been proved true by Janusz Czelakowski (who I have met at conference and have referenced). While still to be published in a journal, and hence properly peer reviewed, it has been three years in the coming, and has survived/grown-from a few rounds in the community, Stack Overflow and two rounds on Research Gate. The currently unbroken version is on Research Gate. He uses Universal Algebra (in this case Peano Arithmetic) and essentially Formal Set Theory.
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A couple of years ago he published a proof of the Twin Prime conjecture, using the same lemma and forcing methods. It was flawed, and retracted.

https://link.springer.com/article/10.1007/s11225-022-10017-2
External Quote:
Home > Studia Logica > Article

RETRACTED ARTICLE: The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic (I)

Open access
Published: 25 October 2022

Volume 111, pages 357–358, (2023)
Cite this article

22 November 2022 This article was retracted on 22 November 2022.
In my experience, when ageing mathematicians start to get a bit too obsessed with the power of some particular result, and want to apply it everywhere, and their first one is false, I update my priors, and hold off until someone like Terence Tao gives it the thumbs up before paying too much attention to it. At least these two papers don't seem to be based on sieve theory, most of the cranky proofs I've encountered have completely misunderstood that field, and then run with it.
 
In my experience, when ageing mathematicians start to get a bit too obsessed with the power of some particular result, and want to apply it everywhere, and their first one is false, I update my priors, and hold off until someone like Terence Tao gives it the thumbs up before paying too much attention to it. At least these two papers don't seem to be based on sieve theory, most of the cranky proofs I've encountered have completely misunderstood that field, and then run with it.
Terence Tao is a giant (and standing on giant's shoulders).
 
A couple of years ago he published a proof of the Twin Prime conjecture, using the same lemma and forcing methods. It was flawed, and retracted.

https://link.springer.com/article/10.1007/s11225-022-10017-2
External Quote:
Home > Studia Logica > Article

RETRACTED ARTICLE: The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic (I)

Open access
Published: 25 October 2022

Volume 111, pages 357–358, (2023)
Cite this article

22 November 2022 This article was retracted on 22 November 2022.
In my experience, when ageing mathematicians start to get a bit too obsessed with the power of some particular result, and want to apply it everywhere, and their first one is false, I update my priors, and hold off until someone like Terence Tao gives it the thumbs up before paying too much attention to it. At least these two papers don't seem to be based on sieve theory, most of the cranky proofs I've encountered have completely misunderstood that field, and then run with it.
I know, but this one is surviving so far? @FatPhil Have you got the paper? I have pdf, but can't get again for some reason. WTF? Has he withdrawn???? [...Czelakowski has been a legend in UA) Hence the ?
 
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I know, but this one is surviving so far? @FatPhil Have you got the paper? I have pdf, but can't get again for some reason. WTF? Has he withdrawn???? [...Czelakowski has been a legend in UA) Hence the ?
It's probably way beyond my ken anyway.
 
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